Finally, we connect the convergence result to the initially stated Itô SDE ().
Under the assumptions of thm:ess-m-diss, the theory of Generalized Dirichlet Forms developed by Stannat (see [1]}) yields the existence of a Hunt process
\(\mathbf {M} = (\Omega ,\mathcal {F},(\mathcal {F}_t)_{t\ge 0},(X_t,Y_t), (P_{(x,y)})_{(x,y)\in \mathbb {R}^{d_1}\times \mathbb {R}^{d_2}})\) 
